Abstract: The asymptotic behavior of the best
-approximation of the kernels by algebraic
polynomials is obtained. These results allow to construct for example the best
quadrature formula that uses integrals over n
subintervals of equal length for classes of functions with bounded rth derivative.
Keywords and phrases: approximation by algebraic polynomials, best one-sided approximation, spline, Favard constant, truncated power, asymptotic equations
